Nov 06 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <6>
R1C2 is the only square in row 1 that can be <5>
R1C3 is the only square in row 1 that can be <6>
R2C7 is the only square in row 2 that can be <7>
R2C6 is the only square in row 2 that can be <9>
R3C8 is the only square in row 3 that can be <4>
R4C4 is the only square in row 4 that can be <7>
R4C2 is the only square in row 4 that can be <9>
R4C1 is the only square in row 4 that can be <1>
R4C9 is the only square in row 4 that can be <6>
R6C4 is the only square in row 6 that can be <1>
R8C7 is the only square in row 8 that can be <5>
Squares R1C5 and R3C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C5 - removing <2> from <279> leaving <79>
R9C5 - removing <2> from <279> leaving <79>
Squares R4C6 and R6C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C6 - removing <8> from <348> leaving <34>
Squares R1C5 and R3C5 in block 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C4 - removing <2> from <2348> leaving <348>
R2C4 - removing <2> from <238> leaving <38>
Intersection of column 3 with block 1. The value <3> only appears in one or more of squares R1C3, R2C3 and R3C3 of column 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C2 - removing <3> from <1238> leaving <128>
Intersection of column 7 with block 3. The value <3> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C8 - removing <3> from <1238> leaving <128>
Squares R2C3 and R2C9 in row 2 and R8C3 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 3 and 9 can be removed.
R3C3 - removing <1> from <138> leaving <38>
R9C3 - removing <1> from <1489> leaving <489>
Squares R2C1 and R6C1 in column 1 and R2C9 and R6C9 in column 9 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in rows 2 and 6 can be removed.
R6C2 - removing <8> from <368> leaving <36>
R2C3 - removing <8> from <138> leaving <13>
R2C4 - removing <8> from <38> leaving <3>
R6C6 - removing <8> from <58> leaving <5>
R6C8 - removing <8> from <2358> leaving <235>
R2C3 can only be <1>
R1C6 can only be <4>
R4C6 can only be <8>
R1C4 can only be <8>
R9C6 can only be <6>
R8C3 can only be <4>
R4C8 can only be <5>
R8C4 can only be <2>
R8C1 can only be <6>
R8C9 can only be <1>
R9C4 can only be <4>
R8C6 can only be <3>
R6C1 can only be <8>
R6C9 can only be <2>
R2C1 can only be <2>
R5C2 can only be <3>
R6C8 can only be <3>
R2C9 can only be <8>
R3C2 can only be <8>
R3C3 can only be <3>
R7C2 can only be <2>
R3C7 can only be <2>
R3C5 can only be <1>
R1C7 can only be <3>
R9C7 can only be <8>
R1C8 can only be <1>
R5C8 can only be <8>
R6C2 can only be <6>
R7C8 can only be <7>
R9C2 can only be <1>
R7C5 can only be <9>
R9C8 can only be <2>
R9C3 can only be <9>
R7C7 can only be <6>
R1C5 can only be <2>
R7C3 can only be <8>
R9C5 can only be <7>
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